The rectangular floor of a classroom is 30 feet in length and 33 feet in width. A scale drawing of the floor has a length of 10 inches. What is the perimeter, in inches, of the floor in the scale drawing?

The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here: A certain type of bacteria doubles every hour

Now number of hours between 9-12 pm

is 15 hours

if at 9 a.m the amount of bacteria is x then we have in 15 hours

at t=1 we have the number of bacteria was

T=2×15

=30

Similarly we have for t=15 we get

T=15×2¹⁵

Hence, The equation we get for the amount of bacteria with  with time T

T(t)=15×2ⁿ where n is the number of hours.

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Answer: 1, 2, 3, 6, 1

Step-by-step explanation:

When listing all the factors for 18, 30 ,54....

18 , 30 , 54 to find the common factors. The common factors for 18,30,54 18 , 30 , 54 are 1,2,3,6 1 , 2 , 3 , 6 . The GCF (HCF) of the numerical factors 1,2,3,6 1 , 2 , 3 , 6 is 6 .

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The area and the angle are matched as below.

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

A circle is a two-dimensional figure with a radius and circumference of 2πr.

The area of a circle is πr².

We have,

Diameter = 10 in

Radius = 5 in

Area of the circle in sector = 360°

πr² = 360

π x 5² = 360

25π in² = 360° _____(1)

Now,

From (1),

25π in² = 360°

Divide both sides with 8.

25/8 π in² = 45°

From (1),

25π in² = 360°

Divide both sides with 18.

25/18 π in² = 20°

From (1),

25π in² = 360°

Divide both sides with 36.

25/36 π in² = 10°

Thus,

Area        Angle

25/8 π in² = 45°

25/18 π in² = 20°

25/36 π in² = 10°

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A mean computed in such a way that each data value is given a weight reflecting its importance is referred to as A weighted mean.

The weighted mean is defined as a type of mean that is calculated by multiplying the weight associated with a particular event or outcome and the associated with the quantitative outcome and then summarizing all the products together.

For each data point to contribute equally to the final mean, some data points contribute more weight than others.

The weighted mean is calculated by multiplying the weight with the quantitative outcome and adding all the products.

weighted average= The sum of variables/sum of all weights.

if the variables are denoted by x and their weights are denoted by y, then we have:

Weighted average = Σ(xy)/Σy

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The predicted femur length is 69 cm

From the question, we have the following parameters that can be used in our computation:

The scatter plot

On the scatter plot, we have

x = the length of two peoples femur (the long leg bone in thigh)

y = height in centimeters

So, we have

Height = 218 cm

From the graph, we have

x = 69

Hence, the femur length is 69 cm

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The required time duration is  0.13 s

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

[tex]h(t)=-5t^2 + v_{0}t+h_{0}[/tex]

Substitute given the values

2=-5t² + 15 t+0

=> 5t² -15t+2 =0

On solving this quadratic equation ,w e get

t= 0.13 s

The required time duration is  0.13 s

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Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.

A relationship of two expresses or integers that is neither equal in mathematics is referred to as an inequality. Furthermore, inequity results from imbalance. In math and science, an inequalities establishes the connection between two ou alors elements. Egality and inequality are not the same. Use the not equal symbol most frequently when two quantities are not equal (). Values of any size can be examined using a variety of inequalities. By changing the two sides until only the variables are left, many straightforward inequalities can be solved. However, a number of factors support inequality: Both sides' 0 are split or added. Exchange the left and the right.

given

2(x- 9 ) = -10   ( given )

= 2x - 18 = -10   ( multiplication property )

= 2x = -10 + 18  ( subtraction property )

2x = 8 ( division property )

x = 4

Because of this, we apply a variety of equality characteristics, such as the multiplication, subtraction, and division properties.

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Answer: The team's time on the final run can be found by successively multiplying their first time by (1 - 0.512) twice:

First run time: 4.85 minutes

Second run time: 4.85 * (1 - 0.512) = 2.37 minutes

Third run time: 2.37 * (1 - 0.512) = 1.15 minutes (rounded to the nearest hundredth)

So the team's time on their final run was 1.15 minutes.

Step-by-step explanation:

The correct answer is option A. 2 1/8 when reduced to the lowest terms.

To subtract 3 1/4 - 1 1/8, we need to convert the fractions to a common denominator. The common denominator for 3 1/4 and 1 1/8 is 8. To convert 3 1/4 to 8, we multiply both the numerator and denominator by 2, resulting in 6/8. To convert 1 1/8 to 8, we multiply both the numerator and denominator by 8, resulting in 8/8.

Now we have two fractions with a common denominator of 8. To subtract them, we subtract the numerators and keep the same denominator. We have 6/8 - 8/8, which is -2/8. To reduce this fraction to the lowest terms, we divide the numerator and denominator by the greatest common factor (GCF), which is 2. -2/8 divided by 2 is -1/4. Finally, we add -1/4 to 1 1/8 to get the answer 2 1/8.

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Value of expression 1 + 1 = 2

Addition is the process of adding two or more items together. In math, addition is the method of calculating the sum of two or more numbers.

Given expression,

1 + 1

+ is sign of Addition, Adding the numbers,

1 + 1 = 2

Hence, 2 is the value of expression 1 + 1.

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The vertex form of quadratic equation is y = a(x - 0)² + 7 and the standard form of quadratic equation is y = 0x² + 7

The vertex form of a quadratic equation is an equation written in the form:

f(x) = a(x - h)² + k,

where (h, k) is the vertex of the parabola represented by the equation. The variable x represents the input value, f(x) represents the output value, a represents the coefficient of the x² term, h represents the x-coordinate of the vertex, and k represents the y-coordinate of the vertex. The vertex form of a quadratic equation is useful for easily identifying the location and shape of the parabola represented by the equation, especially if the parabolic function has a vertex that is not at (0,0).

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

To find the vertex form of this equation, we need to find the vertex first. To do this, we can average the x-values of the maximum and minimum points in the table, which gives us the x-coordinate of the vertex. In this case, the maximum and minimum points are (1, 7) and (-1, -9), so the x-coordinate of the vertex is (1 + -1)/2 = 0.

Next, we can find the y-coordinate of the vertex by evaluating f(0), which gives us 7.

So, the vertex of the parabola is (0, 7).

Using this information, we can write the vertex form of the equation:

y = a(x - 0)² + 7

To find the standard form of the equation, we need to expand the vertex form and simplify.

y = a(x² - 0x) + 7

y = ax² + 7

We can then find the value of a by using any one of the points in the table. Let's use the point (1, 7):

7 = a(1²) + 7

7 = a + 7

a = 0

So, the standard form of the equation is:

y = 0x² + 7

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Answer:

The interval notation for the set of all numbers greater than or equal to 1 and less than 6 is [1, 6).

Step-by-step explanation:

The measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

The interior angles of a regular pentagon measure 108 degrees each. Therefore, if we have two regular pentagons, the right triangle formed by the two pentagons will have two angles that are equal to 108 degrees each.

These two angles are the complement of each other, meaning they add up to 90 degrees. Therefore, one of the angles in the right triangle formed by the two pentagons is 72 degrees, and the other is 18 degrees.

So, the measures of the angles in the right triangle formed by the two regular pentagons are 18 degrees and 72 degrees.

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Cosine of ∠U is 28/53 in proper fraction, 28/53 in improper fraction, 0.52609 in whole number.

The cosine of an angle in a right triangle can be found using the ratio of the adjacent side to the hypotenuse. In this triangle, the adjacent side to ∠U is 28 and the hypotenuse is 53.

cos(∠U) = adjacent side ÷ hypotenuse = 28 ÷ 53 = 28/53

So, the cosine of ∠U is 28/53, written as a proper fraction.

Now let's convert cosine of ∠U is 28/53 in improper fraction:

The cosine of ∠U, which is 28/53, can be expressed as an improper fraction by dividing both the numerator and denominator by their greatest common factor.

gcd(28, 53) = 1, so the fraction cannot be further simplified.

Therefore, the cosine of ∠U, expressed as an improper fraction, is 28/53.

Now let's convert cosine of ∠U is 28/53 in whole number:

The cosine of ∠U, which is 28/53, can be expressed as a whole number by dividing the numerator by the denominator.

28 ÷ 53 = 0.526087

So, the cosine of ∠U expressed as a whole number is approximately 0.52609

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_____ The given question is not correct, so correct Question is:

Find the cosine of ∠U in Triangle UTV with side:

UV=28

VT=45

TU=53

Simplify your answer and write it as a proper fraction, improper fraction, or whole number.

Answer:

XZ=65

Step-by-step explanation:

so half of the circle would be 180

we need XZ and we know that YW+WX+XZ= 180

we also know that WX and YZ are parallel

WX=50

YW=XZ

YW+XZ=2XZ

WX+2XZ=180

50+2XZ=180

2XZ=130

XZ=65

Answer:

25

Step-by-step explanation:

diameter YZ = 50

OZ = OX = 25

thus, mXZ= 25

The two sequences of transformations of ΔABC that exhibit the congruence between the two triangles include the following:

A. a rotation of 180° about the origin and a translation of 1 unit left.

E. a reflection across the x-axis, a reflection across the y-axis, and a translation 1 unit left.

In Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Furthermore, the mapping rule for the rotation of a geometric figure about the origin is given by this mathematical expression:

(x, y)                  →     (-x, -y)

Point A = (-6, 2)  →  Point A' = (-(-6), -(2)) = (6, -2).

By translating the pre-image of triangle A'B'C' horizontally left by 1 unit, the coordinate A" of the image of triangle A'B'C' include the following:

(x, y)                               →                  (x - 1, y - 7)

Coordinate A' = (6, -2)   →    Coordinate A'' (6 - 1, -2) = (5, -2)

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Value of variable x = 13/√2

Value of variable y = 13/√2

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle. The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

Given,

In the right triangle ABC

AC = 13

AB = x

BC = y

∠C = 45°

Sin 45° = AB/AC

1/√2 = x/13

x = 13/√2

AB = 13/√2

Tan 45° = AB/BC

1 = (13/√2)/y

y = 13/√2

BC = 13/√2

Hence, 13/√2 is the value of both variables x and y.

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Answer:

To calculate the total amount of carbon dioxide emitted over the course of 15 years, we can start with the initial amount of 92,000 kilotons and multiply by 0.95 (the reduction factor) each year.

Step-by-step explanation:

Year 1: 92,000 kilotons

Year 2: 92,000 * 0.95 = 87,400 kilotons

Year 3: 87,400 * 0.95 = 82,990 kilotons

and so on, until year 15.

To find the total amount of carbon dioxide emitted over the course of 15 years, we need to sum up the emissions for each year:

92,000 + 87,400 + 82,990 + ... + (92,000 * 0.95^14) = 92,000 * (1 + 0.95 + 0.95^2 + ... + 0.95^14)

This is a finite geometric series and can be calculated using the formula for the sum of a finite geometric series:

S = a * (1 - r^n) / (1 - r),

where S is the sum, a is the first term, r is the common ratio, and n is the number of terms.

For this series, a = 92,000, r = 0.95, and n = 15. Plugging these values into the formula, we get:

S = 92,000 * (1 - 0.95^15) / (1 - 0.95)

S = 92,000 * (1 - 0.556774) / 0.05

S = 92,000 * 0.443226 / 0.05

S = 92,000 * 8.86452

S = 814,178.24 kilotons

Rounding to the nearest whole number, the country would emit 814,178 kilotons of carbon dioxide over the course of 15 years.

Explanation:

First we add up those numbers

2+6+9+56+63+68 = 204

Then divide by 6 because there are 6 values in this list.

204/6 = 34

Answer:34

Step-by-step explanation:It's obtained by simply dividing the sum of all values in a data set by the number of values.

The expression that can represent how many more cans were collected is 8n - 7 > 6n + 3, which is in fact an inequality.

An inequality in math is an algebraic expression that represents, well, inequality. It shows a relationship between two values or expression, which aren't equal to each other. It is used to compare two values/expression, showing if one is greater than, less than, or simply not equal to another. Thus, we would use a mathematical symbol of <, >, ≤, ≥, or ≠ to express an inequality.

Since students in Mr. Juarez's homeroom collected more cans than students in Ms. Wade's homeroom do, you can use the symbol > in your inequality. The number of cans collected in Mr. Juarez's homeroom is 8n − 7, while the number of cans collected in Ms. Wade's homeroom is 6n + 3. Therefore, your inequality would be 8n - 7 > 6n + 3.

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The surface area of each face is 4 square inches.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

A regular octahedron has a surface area of 32 square inches.

That means

all sides are equal.

The surface area of each face is,

= 32/8

= 4 square inches.

Therefore, the required area is 4 square inches.

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To make 5 pizzas, Paula will use 45 sauce and 30 cheese.

Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.

The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.

Given,

Paula uses 18 sauce and 12 cheese to make two pizzas.

Ingredients needed to make one pizza = 18/2 sauce and 12/2 cheese

                                                                = 9 sauce and 6 cheese

Ingredients needed to make 5 pizzas = 9 × 5 sauce and 6× 5 cheese

                                                               = 45 sauce and 30 cheese

Hence, 45 sauce and 30 cheese is needed to make 5 pizzas.

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Answer: 23/72

Step-by-step explanation:

180 degrees = half of circle

5 degrees = 1/72 of circle

5 degrees times 23 = 115 degrees

1/36*23 = 23/72

Answer:

23/72 of a circle

Step-by-step explanation:

4×sector=circle

90÷360=1/4

so,

115/360=23/72

Answer:

b

Step-by-step explanation:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²

∠AFB = 73° is the angles of a triangles .

What does a math angle mean?

An angle is made up of two rays (half-lines) that have a shared termination. The rays serve as the angle's sides, occasionally serving as the angle's legs and occasionally serving as its arms, while the latter is referred to as the vertex of the angle.

because the angles of a triangles add up to 180 degree

      m∠A = 39° ,  m∠ADC = 107°

   so ∠c = 180 - 107 - 39

               = 34°

     BE ≅ BC

         ∠C = ∠E = 34°

        SO ∠EDF = 180 - 107 = 73°

   So ∠DEF = 180 - 34 - 73 = 73°

  Because m∠DFE and ∠AFB are vertical angle

  so  ∠DFE = ∠AFB

     ∠AFB = 73°

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As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

The biggest integer that is able to divide two or more quantities is known as the highest common factor (HCF) or greatest common factor. Highest refers to the biggest or greatest number. The sharing a common meaning of two or more integers. Feature is an integer that can be used to divide a whole number (a divisor). Write each integer as the sum of one's main characteristics in step one.  Step 3: The HCF of said given integers is the greatest number that can be found among the common factors.

given

1. It is assumed that when Helen thinks of two numbers, they have corresponding HCF and LCM values of 5 and 12.

2. The smallest common multiple shared by two numbers is referred to as the least common number.

LCM of 4 and 6 is 12, for instance.

3. The highest number that divides the two selected numbers, leaving a residue of 0, is referred to as the highest common factor.

HCF of 6 and 8 is 2, for instance.

4. Given that the LCM of Helen's two chosen numbers is 12, even multiples of 12 are the two numbers' common multiples. In light of this, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, and so forth.

5.The only numbers that may be divided by 5 are 60 and 120. All other numbers have HCF values other than 5. 60 and 120 have an HCF of 60, but not 5.

As a result, it is evident from the steps above that it is impossible to have two numbers with the same LCM and HCF as 12 and 5, respectively.

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The length of the line segment is approximately 12.04 units. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows: d = √((x2 - x1)^2 + (y2 - y1)^2)

The length of a line segment in a two-dimensional x-y coordinate plane can be found using the distance formula. This formula calculates the distance between two points, (x1, y1) and (x2, y2), on the line segment. The formula is as follows:

d = √((x2 - x1)^2 + (y2 - y1)^2)

In this case, the line segment extends from the point (2, 8) to the point (12, 2). By plugging these values into the formula, we find that:

d = √((12 - 2)^2 + (2 - 8)^2) = √(100 + 36) = √136 = 12.04

So, the length of the line segment is approximately 12.04 units. This formula is useful for finding the distance between any two points in a two-dimensional plane and can be used in various fields such as geometry, physics, and engineering. The formula is based on the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

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Complete question:

What is the length of the line segment in the first quadrant of an x-y coordinate plane that extends from (2, 8) to (12, 2)?

Answer:

its D 136

Step-by-step explanation:

khan

Answer:

No Solution.

Step-by-step explanation:

To solve for x in this equation, we need to simplify both sides of the equation and make them equal.

Starting with the left-hand side:

5 + x - 14 = x - 7

Adding 14 to both sides:

5 + x = x + 7

Subtracting x from both sides:

5 = 7

5 does not equal 7.

Therefore, the value of x is no solution.

Answer:

there is no solution for this, if you solve you will get 0=2 (This is also called a contradiction)

Step-by-step explanation:

5+x-14=x-7

5-14 = -9

-9+x=x-7

x-9=x-7

+9     +9

x=x+2

-x  -x

0 = 2